Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems

In this paper, we introduce a new hybrid inertial accelerated algorithm with a line search technique for solving fixed point problems for demimetric mapping and split equilibrium problems in Hilbert spaces. The algorithm is inspired by Tseng’s extragradient method and the viscosity method. Then, we...

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Autor principal:	Yanlai Song
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	strong convergence split equilibrium problem demimetric mapping hybrid inertial accelerated algorithms Armijo-like step size rule Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/dcaf946862034c56b7e5ed28e83d6659
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id	oai:doaj.org-article:dcaf946862034c56b7e5ed28e83d6659
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spelling	oai:doaj.org-article:dcaf946862034c56b7e5ed28e83d66592021-11-11T18:14:48ZHybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems10.3390/math92126802227-7390https://doaj.org/article/dcaf946862034c56b7e5ed28e83d66592021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2680https://doaj.org/toc/2227-7390In this paper, we introduce a new hybrid inertial accelerated algorithm with a line search technique for solving fixed point problems for demimetric mapping and split equilibrium problems in Hilbert spaces. The algorithm is inspired by Tseng’s extragradient method and the viscosity method. Then, we establish and prove the strong convergence theorem under proper conditions. Furthermore, we also give a numerical example to support the main results. The main results are new and the proofs are relatively simple and different from those in early and recent literature.Yanlai SongMDPI AGarticlestrong convergencesplit equilibrium problemdemimetric mappinghybrid inertial accelerated algorithmsArmijo-like step size ruleMathematicsQA1-939ENMathematics, Vol 9, Iss 2680, p 2680 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	strong convergence split equilibrium problem demimetric mapping hybrid inertial accelerated algorithms Armijo-like step size rule Mathematics QA1-939
spellingShingle	strong convergence split equilibrium problem demimetric mapping hybrid inertial accelerated algorithms Armijo-like step size rule Mathematics QA1-939 Yanlai Song Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems
description	In this paper, we introduce a new hybrid inertial accelerated algorithm with a line search technique for solving fixed point problems for demimetric mapping and split equilibrium problems in Hilbert spaces. The algorithm is inspired by Tseng’s extragradient method and the viscosity method. Then, we establish and prove the strong convergence theorem under proper conditions. Furthermore, we also give a numerical example to support the main results. The main results are new and the proofs are relatively simple and different from those in early and recent literature.
format	article
author	Yanlai Song
author_facet	Yanlai Song
author_sort	Yanlai Song
title	Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems
title_short	Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems
title_full	Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems
title_fullStr	Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems
title_full_unstemmed	Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems
title_sort	hybrid inertial accelerated algorithms for solving split equilibrium and fixed point problems
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/dcaf946862034c56b7e5ed28e83d6659
work_keys_str_mv	AT yanlaisong hybridinertialacceleratedalgorithmsforsolvingsplitequilibriumandfixedpointproblems
_version_	1718431914520477696

Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems

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